Last week we described the rationale that led to the reshuffling of encounters between every turn.
This resulted in one playtester questioning whether the order which the player draws their encounter card affects the odds of drawing the special character encounter. So we’ll go through the math here quickly (tl;dr: the order doesn’t matter).
This scenario is mathematically equivalent to drawing straws, except the short straw wins instead of loses. Although we have 5 encounter cards in each area, we can simplify the math by working with 3 straws – the same logic can be applied at any number of straws.
==The first player==
This player chooses 1 of 3 straws – one of which wins. This player uncomplicatedly has a 1 in 3 chance of winning (1/3rd).
==The second player==
This player chooses 1 of the 2 remaining straws.
In 1 out of 3 cases (1/3rd), the winning straw has already been drawn, and the player cannot win.
In 2 out of 3 cases (2/3rd), the player will be drawing 1 of 2 straws, one of which wins.
This player wins in half othe 2 out of 3 cases. Half of 2/3rds is 1/3rd – the same odds as the first player.
==The final player==
This player gets the remaining straw. This player wins every time neither of the other players win. Given the 1st player will win 1/3rd of games, the 2nd player will also win 1/3rd of games – the final 1/3rd of games will be won by the final player.
Bringing this back to Aethermon, though this logic we can see that it does not matter whether you’re the first play to draw an encounter or the last player – the odds of receiving any individual card does not change.
I promise no math next week AetherRen!